<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: center;"><p>A stone is thrown from point \(P\) on top of a cliff. As it travels through the air, it follows a curved path, reaching a maximum height at point \(Q\) before falling into the sea. The table below shows the height \(y\) (in metres) of the stone at various horizontal distances \(x\) (in metres) from the point it was thrown:</p></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1775551572377-bxpp36jzjya.png" style="max-width: min(300px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div></div></div></div>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 560px;"><colgroup><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center">\(x\)</th><th style="text-align: center; --cell-justify: center">\(1\)</th><th style="text-align: center; --cell-justify: center">\(2\)</th><th style="text-align: center; --cell-justify: center">\(4\)</th><th style="text-align: center; --cell-justify: center">\(6\)</th><th style="text-align: center; --cell-justify: center">\(8\)</th><th style="text-align: center; --cell-justify: center">\(10\)</th><th style="text-align: center; --cell-justify: center">\(12\)</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">\(y\)</td><td style="text-align: center; --cell-justify: center">\(7\)</td><td style="text-align: center; --cell-justify: center">\(16\)</td><td style="text-align: center; --cell-justify: center">\(24\)</td><td style="text-align: center; --cell-justify: center">\(24\)</td><td style="text-align: center; --cell-justify: center">\(16\)</td><td style="text-align: center; --cell-justify: center">\(0\)</td><td style="text-align: center; --cell-justify: center">\(-24\)</td></tr></tbody></table></div></div>
<p>It is given that&nbsp;\(x\) and \(y\) are related by the equation \(y = mx^2 + nx\), where&nbsp;\(m\) and \(n\) are constants.</p>
<p>Use this information to:</p>
<ol class="i-list"><li data-list-item-id="item-i"><div class="list-item-content"><span class="list-item-text">draw the straight-line graph of \(\frac{y}{x}\) against \(x\) and estimate the values of \(m\) and \(n\).</span></div></li><li data-list-item-id="item-ii"><div class="list-item-content"><span class="list-item-text">determine which value of \(y\) is incorrect and estimate its correct value.</span></div></li><li data-list-item-id="item-iii"><div class="list-item-content"><span class="list-item-text">estimate the horizontal distance from the cliff when the stone is at point \(R\).</span></div></li><li data-list-item-id="item-iv"><div class="list-item-content"><span class="list-item-text">estimate the maximum height reached by the stone.</span></div></li></ol>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1775549390753-ag7pmkj47wl.png" style="max-width: min(370px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>

It is given that \(x\) and \(y\) are related by the equation \(y = mx^2 + nx\), where \(m\) and \(n\) are constants.

draw the straight-line graph of \(\frac{y}{x}\) against \(x\) and estimate the values of \(m\) and \(n\).

determine which value of \(y\) is incorrect and estimate its correct value.

estimate the horizontal distance from the cliff when the stone is at point \(R\).

estimate the maximum height reached by the stone.

Linear Law

Linear Law